Problem 3 . Long-term interest rates, such as the US 10-year Treasury rates, are believed

to be random walk. That is, the best forecast of future rates is today's rate. Here, you are asked to

evaluate the one-quarter-ahead (consensus) forecasts of the 10-year Treasury rates from a panel of

professional forecasters. More specifically, let quarter t be the quarter in which the forecasters report

their forecasts of the 10-year Treasury rate for quarter t+1. As such, let At+1 be the actual rate in

quarter t+1, and Pt+1 be the professional (consensus) forecast of At+1 made in quarter t. In addition, let

Rt+1 be the random walk forecast of At+1.

Using the results from Eviews (given below) to answer the following questions:

a. Find and interpret the bias proportion and the variance proportion.

b. Are the professional forecasts unbiased? Write down the test equation, the null and alternative

hypotheses, the decision rule, and your conclusion.

c. Are the professional forecasts free of systematic bias? Write down the test equation, the null and

alternative hypotheses, the decision rule, and your conclusion.

d. Are the professional forecasts more informative than the random walk forecasts? Write down the

test equation, the null and alternative hypotheses, the decision rule, and your conclusion.

e. Calculate Theil's U coefficient and explain what it implies.

f. Are the professional forecasts more accurate than the random walk forecasts in terms of

MSE? Write down the test equation, the null and alternative hypotheses, the decision rule,

and your conclusion.